A constructive differential game approach to collision avoidance in multi-agent systems

The problem of steering a team of agents from their initial positions to a predefined end-configuration while avoiding collisions is formulated as a differential game. A method for approximating the solution of the differential game is then presented, providing ε-Nash strategies. It is shown that approximate solutions are sufficient to guarantee that the task of reaching the final configuration while avoiding collisions is achieved. The theory is illustrated by simulations.